Question

The number of gram molecule of oxygen in ${ 6.022\times { 10 }^{ 24 } } { CO }$ molecules is:
(a) ${ 10 }$ gm molecules
(b) ${ 5 }$ gm molecules
(c) ${ 1 }$ gm molecules
(d) ${ 0.5 }$ gm molecules

Answer 1

Hint: The gram molecule is defined as the number of molecules present in one mole of that substance instead of atoms.
Gram molecular weight:- It is defined as the mass of one mole of a compound equal in grams to the molecular weight.

Complete step-by-step answer:

The number of gram molecules in ${ CO }$ molecule is equal to half the number of gram atoms of ${ CO }$ atom
Number of oxygen atoms = Number of ${ CO }$ molecules = ${ 6.022\times { 10 }^{ 24 } }$
${ 1 }$ oxygen molecule is composed of two oxygen atoms
So, number of oxygen molecules = Half the number of oxygen atoms = ${ 1\div 2\times } { 6.022\times { 10 }^{ 24 } }$
= ${ 3.011\times { 10 }^{ 24 } }$

Now, the moles of oxygen gas = ${ 3.011\times 10 }^{ 24 }\div { 6.022\times 10 }^{ 23 }$ = 5 moles
As we know that ${ 1 }$ mole = ${ 1 }$ gram of compound
So, ${ 5 }$ moles will be equal to ${ 5 }$ grams of oxygen
Hence, the number of gram molecules of oxygen in ${ 6.022\times {10}^{24}} {CO}$ molecules is ${ 5 }$.

Additional Information:
The formula of mole concept can be written as:
A number of atoms or molecules = Avogadro’s no.
The relationship between amu and gram is; 1 amu = ${ 1 } g / { N }_{ a } = { 1.66\times { 10 }^{ -24 } }$
Therefore, the mass of one mole of an element is equal to its atomic mass in grams.
A number of moles = Mass of the sample/molar mass.

Note: The possibility of making a mistake in this question is that you may get confused between the moles given by the CO molecules and Avogadro’s number and you must know all the formulas of the mole concept.